lib: add some pure word lemmas found in proof/*

Preparation for removing duplicate word lemmas. These new lemmas
don't belong in the AFP word library, so we hook in to
`Word_Lemmas_Prefix` to expose them to our own theories.

lib/ARM/WordSetup.thy

@@ -12,7 +12,7 @@
 theory WordSetup (* part of non-AFP Word_Lib *)
 imports
   "../Distinct_Prop"
-  "../Word_Lib/Word_Lemmas_32"
+  "../Word_Lib/Word_Lemmas_32_Internal"
 begin
 
 (* Distinct_Prop lemmas that need word lemmas: *)

lib/ARM_HYP/WordSetup.thy

@@ -12,7 +12,7 @@
 theory WordSetup (* part of non-AFP Word_Lib *)
 imports
   "../Distinct_Prop"
-  "../Word_Lib/Word_Lemmas_32"
+  "../Word_Lib/Word_Lemmas_32_Internal"
 begin
 
 (* Distinct_Prop lemmas that need word lemmas: *)

lib/RISCV64/WordSetup.thy

@@ -12,7 +12,7 @@
 theory WordSetup (* part of non-AFP Word_Lib *)
 imports
   "../Distinct_Prop"
-  "../Word_Lib/Word_Lemmas_64"
+  "../Word_Lib/Word_Lemmas_64_Internal"
 begin
 
 (* Distinct_Prop lemmas that need word lemmas: *)

lib/Word_Lib/Word_Lemmas_32_Internal.thy

@@ -0,0 +1,124 @@
+(*
+ * Copyright 2018, Data61
+ *
+ * This software may be distributed and modified according to the terms of
+ * the BSD 2-Clause license. Note that NO WARRANTY is provided.
+ * See "LICENSE_BSD2.txt" for details.
+ *
+ * @TAG(DATA61_BSD)
+ *)
+
+theory Word_Lemmas_32_Internal
+imports Word_Lemmas_32
+begin
+
+lemmas sint_eq_uint_32 = sint_eq_uint_2pl[where 'a=32, simplified]
+
+lemmas sle_positive_32 = sle_le_2pl[where 'a=32, simplified]
+
+lemmas sless_positive_32 = sless_less_2pl[where 'a=32, simplified]
+
+lemma zero_le_sint_32:
+  "\<lbrakk> 0 \<le> (a :: word32); a < 0x80000000 \<rbrakk>
+   \<Longrightarrow> 0 \<le> sint a"
+  by (clarsimp simp: sint_eq_uint_32 unat_less_helper)
+
+lemmas unat_add_simple = iffD1[OF unat_add_lem[where 'a = 32, folded word_bits_def]]
+
+lemma upto_enum_inc_1:
+  "a < 2 ^ word_bits - 1
+   \<Longrightarrow> [(0:: 'a :: len word) .e. 1 + a] = [0.e.a] @ [(1+a)]"
+  using upper_trivial upto_enum_inc_1_len by force
+
+lemmas upt_enum_offset_trivial =
+  upt_enum_offset_trivial[where 'a=32, folded word_bits_def]
+
+lemmas unat32_eq_of_nat = unat_eq_of_nat[where 'a=32, folded word_bits_def]
+
+declare mask_32_max_word[simp]
+
+lemma le_32_mask_eq:
+  "(bits :: word32) \<le> 32 \<Longrightarrow> bits && mask 6 = bits"
+  by (fastforce elim: le_less_trans intro: less_mask_eq)
+
+lemmas scast_1_32[simp] = scast_1[where 'a=32]
+
+lemmas mask_32_id[simp] = mask_len_id[where 'a=32, folded word_bits_def]
+
+lemmas t2p_shiftr_32 = t2p_shiftr[where 'a=32, folded word_bits_def]
+
+lemma mask_eq1_nochoice:
+  "(x :: word32) && 1 = x
+   \<Longrightarrow> x = 0 \<or> x = 1"
+  using mask_eq1_nochoice len32 by force
+
+lemmas const_le_unat_word_32 = const_le_unat[where 'a=32, folded word_bits_def]
+
+lemmas createNewCaps_guard_helper =
+  createNewCaps_guard[where 'a=32, folded word_bits_def]
+
+lemma word_log2_max_word32[simp]:
+  "word_log2 (w :: 32 word) < 32"
+  using word_log2_max[where w=w]
+  by (simp add: word_size)
+
+(* FIXME: specialize using pow_sub_less_word *)
+lemma mapping_two_power_16_64_inequality:
+  assumes sz: "sz \<le> 4" and len: "unat (len :: word32) = 2 ^ sz"
+  shows "unat (len * 8 - 1) \<le> 127"
+  using pow_sub_less[where 'a=32 and b=3, simplified]
+proof -
+  have len2: "len = 2 ^ sz"
+    apply (rule word_unat.Rep_eqD, simp only: len)
+    using sz
+    apply simp
+    done
+
+  show ?thesis using two_power_increasing_less_1[where 'a=32 and n="sz + 3" and m=7]
+    by (simp add: word_le_nat_alt sz power_add len2 field_simps)
+qed
+
+lemmas pre_helper2_32 = pre_helper2[where 'a=32, folded word_bits_def]
+
+lemmas of_nat_shift_distinct_helper_machine =
+  of_nat_shift_distinct_helper[where 'a=32, folded word_bits_def]
+
+lemmas ptr_add_distinct_helper_32 =
+  ptr_add_distinct_helper[where 'a=32, folded word_bits_def]
+
+lemmas mask_out_eq_0_32 = mask_out_eq_0[where 'a=32, folded word_bits_def]
+
+lemmas neg_mask_mask_unat_32 = neg_mask_mask_unat[where 'a=32, folded word_bits_def]
+
+lemmas unat_less_iff_32 = unat_less_iff[where 'a=32, folded word_bits_def]
+
+lemmas is_aligned_no_overflow3_32 = is_aligned_no_overflow3[where 'a=32, folded word_bits_def]
+
+lemmas unat_ucast_16_32 = unat_signed_ucast_less_ucast[where 'a=16 and 'b=32, simplified]
+
+(* FIXME: generalize? *)
+lemma scast_mask_8:
+  "scast (mask 8 :: sword32) = (mask 8 :: word32)"
+  by (clarsimp simp: mask_def)
+
+lemmas ucast_le_8_32_equiv = ucast_le_up_down_iff[where 'a=8 and 'b=32, simplified]
+
+lemma signed_unat_minus_one_32:
+  "unat (-1 :: 32 signed word) = 4294967295"
+  by (simp del: word_pow_0 diff_0 add: unat_sub_if' minus_one_word)
+
+lemmas two_bits_cases_32 = two_bits_cases[where 'a=32, simplified]
+
+lemmas word_ctz_not_minus_1_32 = word_ctz_not_minus_1[where 'a=32, simplified]
+
+lemmas sint_ctz_32 = sint_ctz[where 'a=32, simplified]
+
+(* FIXME: inline these? *)
+lemmas scast_specific_plus32 =
+  scast_of_nat_signed_to_unsigned_add[where 'a=32 and x="word_ctz x" and y="0x20" for x,
+                                      simplified]
+lemmas scast_specific_plus32_signed =
+  scast_of_nat_unsigned_to_signed_add[where 'a=32 and x="word_ctz x" and y="0x20" for x,
+                                      simplified]
+
+end

lib/Word_Lib/Word_Lemmas_64_Internal.thy

@@ -0,0 +1,17 @@
+(*
+ * Copyright 2018, Data61
+ *
+ * This software may be distributed and modified according to the terms of
+ * the BSD 2-Clause license. Note that NO WARRANTY is provided.
+ * See "LICENSE_BSD2.txt" for details.
+ *
+ * @TAG(DATA61_BSD)
+ *)
+
+theory Word_Lemmas_64_Internal
+imports Word_Lemmas_64
+begin
+
+lemmas unat_add_simple = iffD1[OF unat_add_lem[where 'a = 64, folded word_bits_def]]
+
+end

lib/Word_Lib/Word_Lemmas_Prefix.thy

@@ -17,6 +17,7 @@ section "Word Lemmas that use List Prefix-Order"
 theory Word_Lemmas_Prefix
 imports
   Word_Lemmas
+  Word_Lemmas_Internal
   "HOL-Library.Prefix_Order"
 begin
 

lib/X64/WordSetup.thy

@@ -12,7 +12,7 @@
 theory WordSetup (* part of non-AFP Word_Lib *)
 imports
   "../Distinct_Prop"
-  "../Word_Lib/Word_Lemmas_64"
+  "../Word_Lib/Word_Lemmas_64_Internal"
 begin
 
 (* Distinct_Prop lemmas that need word lemmas: *)